Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras

Abstract

<jats:p>In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras, and matching pre-Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom-algebraic structures.</jats:p>

Matching BiHom-Rota-Baxter Algebras and Related Structures

“…(i) Obviously, compatible BiHom-associative algebras include matching BiHom-associative algebras or totally compatible BiHom-associative algebras. (ii) Matching (Hom)-associative algebras, totally compatible (Hom)-associative algebras and compatible (Hom)-associative algebras given in [17] ( [21]) are special cases of above definitions, when p = q = Id(p = q). (iii) If Ω is a singleton, BiHom-associative algebras introduced in [8] are special cases of matching BiHom-associative algebras and compatible BiHom-associative algebras.…”

“…The notions of matching Hom-Rota-Baxter algebras, matching Hom-(tri)dendriform algebras and matching Hom-pre-Lie algebras are introduced by [21]. The main purpose of this paper is to extend these matching algebraic structures to the BiHom-algebras setting and study the connections between these categories of BiHom-algebras.…”